A complete lesson on using sin, cos and tan to find an unknown side of a right-angled triangle. Designed to come after pupils have been introduced to the trig ratios, and used them to find angles in right-angled triangles. Please see my other resources for complete lessons on these topics. Activities included: Starter: A quick reminder and some questions about using formulae triangles (e.g. the speed, distance, time triangle). This is to help pupils to transfer the same idea to the SOHCAHTOA formulae triangles. Main: A few examples and questions for pupils to try, on finding a side given one side and an angle. Initially, this is done without reference to SOHCAHTOA or formulae triangles, so that pupils need to think about whether to multiply or divide. More examples, but this time using formulae triangles. A worksheet with a progression in difficulty, building up to some challenging questions on finding perimeters of right-angled triangles, given one side and an angle. A tough extension, where pupils try to find lengths for the sides of a triangle with a given angle, so that it is has a perimeter of 20cm. Plenary: A prompt to get pupils thinking about how they are going to remember the rules and methods for this topic. Printable worksheets and answers included. Please review if you buy as any feedback is appreciated! Error on previous version now fixed. If you have bought this already and want the amended version, please message me and I will email the file directly.

A complete lesson on finding an angle in a right-angled triangle using trig ratios. Designed to come after pupils have been introduced to the ratios sin, cos and tan, and have investigated how the ratios vary. Please see my other resources for complete lessons on these topics. Activities included: Starter: Provided with the graph of y=sinx, pupils estimate sinx for different values of x and vice-versa. Main: Slides to introduce use of scientific calculators to find accurate values for angles or ratios. Examples of the basic method of finding an angle given two sides. Includes graphs to reinforce what is happening. Quick questions for pupils to try and provided feedback. A worksheet of questions with a progression in difficulty. Starts with standard questions, then moves on to more challenging ones (eg finding the smallest angle in a non-right-angled, isosceles triangle). Plenary: A final question to check pupils’ understanding, but also with a combinations/logic element. Printable worksheets and answers included. Please review if you buy as any feedback is appreciated!

A complete lesson for first introducing how to find angles in a right-angled triangle using a trig ratio, but as a pupil-led investigation. Intended to come after pupils have practiced identifying hypotenuse/opposite/adjacent and calculating sin/cos/tan. Activities included: Starter: A set of questions to check pupils can correctly calculate sin, cos and tan from a triangle’s dimensions. Main: A structured investigation where pupils: Investigate sin, cos and tan for triangles of different size but the same angles (i.e. similar triangles), by measuring dimensions of triangles and calculating ratios Investigate what happens as the angle varies by measuring dimensions of triangles, calculating ratios, and plotting separate graphs of sin, cos and tan. Using their graphs to estimate angles for conventional SOHCAHTOA questions (i.e. finding an angle given two sides) Plenary: A prompt to get pupils to discuss/reflect on their understanding of the use of trig ratios. Printable worksheets and answers included. Please review if you buy as any feedback is appreciated!

A complete lesson for first introducing the ratios sin, cos and tan. Ideal as a a precursor to teaching pupils SOHCAHTOA. Activities included: Starter: Some basic similarity questions (I would always teach similarity before trig ratios). Main: Examples and questions on using similarity to find missing sides, given a trig ratio (see cover image for an example of what I mean, and to understand the intention of doing this first). Examples, quick questions and worksheets on identifying hypotenuse/opposite/adjacent and then sin/cos/tan for right-angled triangles. A challenging always, sometimes, never activity involving trig ratios. Plenary: A discussion about the last task, and a chance for pupils to share ideas. Printable worksheets and answers included. Please review if you buy as any feedback is appreciated!

A complete lesson on compound interest calculations. Activities included: Starter: A set of questions to refresh pupils on making percentage increases. Main: Examples and quick questions on interest. Examples and a worksheet on compound interest by adding on the interest each year. Examples and a worksheet on compound interest using the direct multiplier method. A challenging set of extension questions. Plenary: A prompt for pupils to think about the graph of compounded savings with time. Printable worksheets and answers included. Please review if you buy as any feedback is appreciated!

A complete lesson (or maybe two) on finding an original amount, given a sale price or the value of something after it has been increased. Looks at both calculator and non-calculator methods. Activities included: Starter: A set of four puzzles where pupils work their way back to 100%, given another percentage. Main: Examples, quick questions for pupils to try and a worksheet on calculator methods for reversing a percentage problem. Examples, quick questions for pupils to try and a worksheet on non- calculator methods for reversing a percentage problem. Both worksheets have been scaffolded to help pupils with this tricky topic. A challenging extension task where pupils form and solve equations involving connected amounts. Plenary: A final question to address the classic misconception for this topic. Printable worksheets and answers included. Please review if you buy as any feedback is appreciated!

A complete lesson on expressing a change as a percentage. Activities included: Starter: A puzzle to remind pupils of how to make a percentage change. Main: Examples and quick questions for pupils to try, on working out the percentage change. A worksheet with a progression in difficulty and a mix of question types. An extension task involving a combination of percentage changes. Plenary: A ‘spot the mistake’ question. Printable worksheets and answers included. Please review if you buy as any feedback is appreciated!

A complete lesson on using calculators to directly make percentage changes, e.g. increasing by 5% by multiplying by 1.05 Activities included: Starter: A recap on making a percentage change in stages, e.g. increasing something by 5% by working out 5% and adding it to the original amount. Main: Examples and quick questions for pupils to try, along with some diagnostic questions to hopefully anticipate a few misconceptions. A worksheet of questions with a progression in difficulty. An extension task/investigation designed to challenge the misconception that you can reverse a percentage increase by decreasing by the same percentage. Plenary: A question in context - working out a restaurant bill including a tip. Printable worksheets and answers included. Please review if you buy, as any feedback is appreciated!

A complete lesson on increasing or decreasing by a percentage. Activities included: Starter: A template for pupils to work out lots of different percentages of £30 Main: Examples and a set of straight-forward questions making percentage changes. A connect 4 game for pupils to play in pairs, taking it in turns to work out percentage changes and win squares on a grid. A few questions to discuss about the game. A puzzle where pupils arrange numbers and percentage change statements to make a loop. Plenary: Some examples looking at making a percentage decrease a different way - eg decreasing by 25% by directly working out 75% Printable worksheets and answers included. Please review if you buy as any feedback is appreciated!

A complete lesson on finding percentages of an amount using non-calculator methods, by relating them to the key percentages of 10%, 25% and 1%. See the cover image to get an idea of the intention of the lesson. Activities included: Starter: A set of questions to recap on finding 50%, 25%, 75%, 10%, 5%, 20% and 1% of an amount. Main: Some slides to introduce the idea of using the key percentages to find other percentages. A worksheet to consolidate these ideas, followed by three flowcharts in the style of the cover image, where pupils are given a starting number and work out all the percentages. The starting numbers get progressively more difficult. I use this as a non-calculator task, but it could be used with calculators too. An extension task where pupils work out some percentages not included in the flowcharts, by combining percentages. Plenary: A great discussion question, looking at four possible ways to calculate 75% of a number. Printable worksheets and answers included. Please review if you buy as any feedback is appreciated!

A complete lesson on finding percentages of an amount using non-calculator methods. Looks at finding 50%, 25%, 75%, 10%, 5%, 20% and 1%. Activities included: Starter: A set of questions where pupils convert the percentages above into their simplified, fraction form. Main: Some examples and quick questions on finding percentages of an amount for pupils to try. A set of questions with a progression in difficulty, from finding simple percentages, to going in reverse and identifying the percentage. The ‘spider diagrams’ are my take on TES user alutwyche’s spiders. An extension task where pupils arrange digits (with some thought) in order to make statements true. Plenary: A nice visual flow chart to reinforce how the calculations required are connected. Printable worksheets and answers included. Please review if you use as any feedback is appreciated!

A complete lesson for first teaching how to find a fraction of an amount. Activities included: Starter: A matching activity, where pupils pair up shapes with the same fraction shaded. Main: Some highly visual examples of finding a fraction of an amount, using bar modelling. Some examples and quick questions for pupils to try (these don’t use bar modelling, but I guess weaker pupils could draw diagrams to help). A set of questions with a progression in difficulty, from integer answers to decimal answers to some sneaky questions where the pupils need to spot that the fraction can be simplified. An extension task where pupils arrange digits (with some thought) in order to make statements true. Plenary: A nice visual odd-one-out puzzle to finish, that may well expose a few misconceptions too. Optional, printable worksheets and answers included. Please review if you buy as any feedback is appreciated!

A complete lesson for first teaching how to divide fractions by fractions. Activities included: Starter: A set of questions on multiplying fractions (I assume everyone would teach this before doing division). Main: Some highly visual examples of dividing by a fraction, using a form of bar modelling (more to help pupils feel comfortable with the idea of dividing a fraction by a fraction, than as a method for working them out). Examples and quick questions for pupils to try, using the standard method of flipping the fraction and multiplying. A set of straightforward questions. A challenging extension where pupils must test different combinations and try to find one that gives required answers. Plenary: An example and explanation (I wouldn’t call it a proof though) of why the standard method works. Optional worksheets (ie everything could be projected, but there are copies in case you want to print) and answers included. Please review if you buy as any feedback is appreciated!

A complete lesson for first teaching how to divide whole numbers by fractions. Activities included: Starter: A set of recap question to test if pupils can simplify improper fractions. Main: Some highly visual examples of dividing by a fraction, using bar modelling (more to help pupils feel comfortable with the idea of dividing by a fraction, than as a method for working them out). Two sets of straightforward questions, the first on dividing by a unit fraction, the second on dividing by a non-unit fraction, moving from integer answers to fractional answers. An extension where pupils investigate divisions of a certain format. Plenary: Two more related examples using bar modelling, to reinforce the logic of the method used for division by a fraction. Answers included to all tasks. Please review if you buy as any feedback is appreciated!

A complete lesson for first teaching how to divide fractions by whole numbers. Activities included: Starter: A simple question in context to help pupils visualise division of fractions by whole numbers. Main: Some example and questions for pupils to try. A set of straightforward questions. A challenging extension where pupils must think a lot more carefully about what steps to take. Plenary: A final example designed to challenge the misconception of division leading to an equivalent fraction, and give a chance to reinforce the key method. Worksheets and answers included. Please review if you buy as any feedback is appreciated!

A challenging set of puzzles, that mainly require pupils to use their knowledge of the properties and area rule of a parallelogram, but also involve finding areas of triangles. Includes a few ideas adapted from other sources, one of which is Don Steward’s superb Median blog, the other I’m afraid I can’t remember. Please review if you like it, or even if you don’t!

A challenging set of puzzles involving equivalent fractions, probably best for high ability secondary groups. Also offers pupils practice of using divisibility tests, simplifying fractions and working systematically. Please review if you like it, or even if you don’t!

A complete lesson for first teaching what mixed numbers and improper fractions are, and how to switch between the two forms. Activities included: Starter: Some quick questions to test if pupils can find remainders when dividing. Main: Some examples and a worksheet on identifying mixed numbers and improper fractions from a pictorial representation. Examples and quick questions for pupils to try, on how to convert a mixed number into an improper fraction. A set of straight forward questions for pupils to work on, with an extension task for those who finish. Examples and quick questions for pupils to try, on how to simplify an improper fraction. A set of straight forward questions for pupils to work on, with a challenging extension task for those who finish. Plenary: A final question looking at the options when simplifying improper fractions with common factors. Worksheets and answers included. Please review if you buy as any feedback is appreciated!

A complete lesson for first teaching how to add and subtract fractions with different denominators. Does include some examples and questions involving simplifying at the end, but doesn’t include adding or subtracting mixed numbers. Activities included: Starter: Some quick questions to test if pupils can find equivalent fractions and identify the lowest common multiple of two numbers. Main: Some examples with diagrams to help pupils understand the need for common denominators when adding. A recap/help sheet of equivalent fractions for pupils to reference while they try some simple additions and subtractions. At this stage, they aren’t expected to find LCMs ‘properly’, just to find them on the help sheet. Some example question pairs on adding or subtracting by first identifying the lowest common denominator, starting with the scenario that the LCM is the product of the denominators, then the scenario that the LCM is one of the denominators, and finally the scenario that the LCM is something else (eg denominators of 4 and 6). A set of straightforward questions with a progression in difficulty. The hardest ones require students to simplify the answer. A challenging extension where pupils must find four digits to fit a given fraction sum. Plenary: A final example designed to challenge the misconception of adding numerators and denominators, and give a chance to reinforce the key method. Worksheets and answers included. Please review if you buy as any feedback is appreciated!

A complete lesson for first teaching how to simplify a fraction. Activities included: Starter: Some quick questions to test if pupils can find the highest common factor of two numbers. Main: A short activity where pupils sort a selection of fractions into two groups, based on whether they are simplified or not. Example question pairs to quickly assess if pupils understand how to simplify. A set of straightforward questions with a progression in difficulty. A challenging extension where pupils must arrange four digits to create fractions that simplify to given fractions. Plenary: Some questions in context to reinforce the key skill and also give some purpose to the process of simplifying fractions. Optional worksheets and answers included. Please review if you buy as any feedback is appreciated!